Teach Latin to help curb knife crime, ran the headline in the Daily Telegraph. No prizes for guessing which politician was behind this sentiment. "I think there's a huge amount we can do in London by promoting the learning of languages including Latin," Boris Johnson was quoted as saying. "I would like to see not only that but I would like to see ancient Greek."

The irony is that I, as a fellow classicist (and a product of Johnson's very own alma mater), have no particular argument with the general idea. Yes, it would be great if Latin and Greek were more widely taught in schools. Yes, education has to form part of the struggle against knife crime. But the notion that learning Latin and Greek might be an integral part of preventing this horrific phenomenon – well, has anyone thought of letting them eat cake?

Johnson has, to be fair, put a great deal of energy into promoting the classics. He is president of the Joint Association of Classical Teachers; he speaks for classics; he campaigns; he broadcasts. He deserves great credit for his efforts. My worry is not that Johnson is a champion of classics, but that he is the only prominent, high-profile champion of classics in this country. And he represents something very particular: a posh, white, public-school, rightwing, blokeish version of classics that, when unchallenged by any other popular view of the subject, does it enormous disservice. If the prevailing feeling is that Latin and Greek are for toffs, then Boris, frankly, is not the man to dispel that notion.

The fact, of course, is that classics is not for toffs. As Latin and Greek have drifted away from school timetables, so many universities have adapted, offering teaching in the languages from scratch: these days, no one need be held back by not having been to the "right school". And, while the Boris version of classics might summon up visions of pipe-smoking dons trading bons mots from Horace in the senior common room, professional classicists these days are more likely to be interested in sexuality and gender; in the implications of ancient colonialism; in ancient notions of humour or national identity or class or a host of other questions that would probably make the traditionalist in Johnson shudder.

Rather than a subject for the posh, classics is a subject for the intellectually ambitious, like Hardy's Jude; or indeed Virginia Woolf, who taught herself Greek so as to be able to read Sophocles in the original. (She wrote about it movingly in her essay On Not Knowing Greek). It is, in short, classless. Mary Beard, professor of ancient history at Cambridge University and the nearest we have to a non-Boris popular champion of the subject, has written fascinatingly in her blog about the working-class classicists of the past – including a fellow called Alfred Williams, born in 1877, who worked in a railway factory and learned Latin and Greek by chalking up irregular verbs on his forge.It's time, then to take the class out of classics. And, while we're at it, we might remember that the ancient world is not a great place to start if you want to reduce knife crime. Does anyone remember how Julius Caesar was murdered?

Charlotte Higgins is author of Latin Love Lessons: Put a Little Ovid in Your Life (Short Books). It's All Greek To Me (also Short Books) is published in October.